Question: How many ways are there to arrange the letters of the word $\text{BA}_1\text{N}_1\text{A}_2\text{N}_2\text{A}_3$, in which the three A's and the two N's are considered different?
Explanation: This is counting the number of ways that six distinct objects can be put in order, so there are $6! = \boxed{720}$ different arrangements.